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Pada sebuah segitiga KLM siku-siku di  L berlaku tan K=31​ dan panjang sisi KL=63​. Tentukan panjang sisi yang lain dan nilai perbandingan trigonometri lainnya!

Pertanyaan

Pada sebuah segitiga KLM siku-siku di  L berlaku tan space straight K equals 1 third dan panjang sisi KL equals square root of 63. Tentukan panjang sisi yang lain dan nilai perbandingan trigonometri lainnya!

D. Kusumawardhani

Master Teacher

Jawaban terverifikasi

Pembahasan

Diketahui

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space K end cell equals cell 1 third end cell row KL equals cell square root of 63 end cell end table  

Segitiga text KLM end text siku-siku di text L end text maka dapat diilustrasikan sebagai berikut.

Berdasarkan definisi tangen, maka dapat ditentukan panjang sisi text LM dan KM end text sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell tan space K end cell equals cell depan over samping equals LM over KL end cell row cell 1 third end cell equals cell fraction numerator LM over denominator square root of 63 end fraction end cell row LM equals cell 1 third square root of 63 end cell row blank equals cell 1 third square root of 9 cross times 7 end root end cell row blank equals cell 1 third left parenthesis 3 right parenthesis square root of 7 end cell row blank equals cell square root of 7 end cell row KM equals cell square root of KL squared plus LM squared end root end cell row blank equals cell square root of open parentheses square root of 63 close parentheses squared plus open parentheses square root of 7 close parentheses squared end root end cell row blank equals cell square root of 63 plus 7 end root end cell row blank equals cell square root of 70 end cell end table 

Ingat definisi trigonometri

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space x end cell equals cell fraction numerator text depan end text over denominator text miring end text end fraction end cell row cell cos space x end cell equals cell fraction numerator text samping end text over denominator text miring end text end fraction end cell row cell csc space x end cell equals cell fraction numerator 1 over denominator sin space x end fraction end cell row cell sec space x end cell equals cell fraction numerator 1 over denominator cos space x end fraction end cell row cell cot space x end cell equals cell fraction numerator 1 over denominator tan space x end fraction end cell end table

text LM end text sisi depan sudut text K end text dan text KL end text sisi samping sudut text K end text maka

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space straight K end cell equals cell LM over KM end cell row blank equals cell fraction numerator square root of 7 over denominator square root of 70 end fraction end cell row blank equals cell 1 over 10 square root of 10 end cell row cell cos space straight K end cell equals cell KL over KM end cell row blank equals cell fraction numerator square root of 63 over denominator square root of 70 end fraction end cell row blank equals cell fraction numerator 3 square root of 7 over denominator square root of 70 end fraction end cell row blank equals cell 3 over 10 square root of 10 end cell row cell cot space straight K end cell equals cell fraction numerator 1 over denominator tan space straight K end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style bevelled 1 third end style end fraction end cell row blank equals 3 row cell sec space straight K end cell equals cell fraction numerator 1 over denominator cos space straight K end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style bevelled fraction numerator 3 square root of 10 over denominator 10 end fraction end style end fraction end cell row blank equals cell fraction numerator 10 over denominator 3 square root of 10 end fraction end cell row blank equals cell 1 third square root of 10 end cell row cell cosec space straight K end cell equals cell fraction numerator 1 over denominator sin space straight K end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style bevelled fraction numerator square root of 10 over denominator 10 end fraction end style end fraction end cell row blank equals cell fraction numerator 10 over denominator square root of 10 end fraction end cell row blank equals cell square root of 10 end cell end table

Dengan demikian, panjang sisi dan perbandingan sisi yang lain adalah sebagai berikut. 

KL equals square root of 63 semicolon space LM equals square root of 7 semicolon space KM equals square root of 70 

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space straight K end cell equals cell 1 over 10 square root of 10 end cell row cell cos space straight K end cell equals cell 3 over 10 square root of 10 end cell row cell cot space straight K end cell equals 3 row cell sec space straight K end cell equals cell 1 third square root of 10 end cell row cell cosec space straight K end cell equals cell square root of 10 end cell end table 

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